If a^2 + b^2 = 2ab, show that log a+b/2 = log a+ log b /2

asked Jul 5, 2023 194k views

5 votes

3.0k points

Please log in or register to add a comment.

3 votes

If a²+b²=2ab therefore:

$\begin{gathered} a^2+b^2-2ab=0 \\ \Leftrightarrow(a-b)^2=0 \\ \Leftrightarrow a=b \end{gathered}$

Therefore:

$\log (a+b)/(2)=\log (2a)/(2)=\log a=(2)/(2)\log a=(\log a+\log a)/(2)=(\log a+\log b)/(2)$

Flat Cat answered Jul 10, 2023

3.3k points

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

3.3m questions

4.2m answers